Trapping Neutral Atoms in the Field of a Vortex Pinned by a Superconducting Nano-disc
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Atom chips made of superconducting material can generate magnetic traps with significantly reduced noise. Recently, several designs for superconducting chips have been theoretically analyzed and experimentally tested for cases with many vortices considered as an average vortex density. Here we show theoretically how the magnetic field of a single vortex, pinned by a superconducting nanodisk of radius \ensuremath{\sim}100 nm and combined with an external bias field parallel to the disk surface, yields a closed three-dimensional trap for cold atoms. The size of the trap and its height above the superconductor surface are typically tens or hundreds of nanometers. We estimate the average lifetime \ensuremath{\tau} of $^{87}\mathrm{Rb}$ (rubidium) atoms (subject to thermal escape and Majorana spin flips) in the range 0.05\char21{}1.0 ms. We model the trap in a quantum adiabatic approximation and apply Fermi's rule to estimate the lifetime of $^{87}\mathrm{Rb}$ atoms in the ground state of this trap. We obtain similar lifetimes \ensuremath{\tau} as in the semiclassical estimate, in the range 0.05\char21{}3.5 ms. We find that \ensuremath{\tau} depends on the gradient ${B}_{0}$ of the vortex's magnetic field according to $\ensuremath{\tau}\ensuremath{\sim}{B}_{0}^{\ensuremath{-}2/3}$.